Question 1110101: Below is the graph of
y=log2x
.
Translate it to become the graph of y=log2(x−4)+3
.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! what you will find is:
log2(x-4) is the same as log2(x), but shifted to the right 4 units on a graph.
an example will show you what i mean.
when x = 6, the value of y = log2(x) is 2.585
when x = 10, the value of y = log2(x-4) is 5.585.
the value of y = log2(x-4) when x = 10 is the same value of y = log2(x) when x = 6, except that the value is 3 units higher.
how is this so?
well, when x = 6, y = log2(x) becomes log2(6) and, when x = 10, y = log2(x-4) becomes y = log2(10 - 6) which becomes log2(6).
the difference is the + 3 added to y = log2(x-4).
it raises the value of y + 3 units to make it y = 5.585, rather than y = 2.585.
here's what the graph of this example looks like.
this relationship happens with all equations, not just log equations.
here's a reference on transformation of algebraic equations.
those rules apply to log functions as well.
https://www.mathsisfun.com/sets/function-transformations.html
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